We report the detection of GeV gamma-ray emission from the molecular cloud complex that surrounds the supernova remnant (SNR) W44 using the Large Area Telescope (LAT) onboard Fermi. While the previously reported gamma-ray emission from SNR W44 is likely to arise from the dense radio-emitting filaments within the remnant, the gamma-ray emission that appears to come from the surrounding molecular cloud complex can be ascribed to the cosmic rays (CRs) that have escaped from W44. The non-detection of synchrotron radio emission associated with the molecular cloud complex suggests the decay of neutral pi mesons produced in hadronic collisions as the gamma-ray emission mechanism. The total kinetic energy channeled into the escaping CRs is estimated to be (0.3--3)x10^{50} erg, in broad agreement with the conjecture that SNRs are the main sources of Galactic CRs.
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